Tesla has named Robyn Denholm, the CFO at the Australian telecom operator Telstra, as its new board chair.

Tesla's CEO and founder, Elon Musk, was forced to step down from his role as chairman of the board as part of a settlement with the Securities and Exchange Commission.

Tesla shares were up as much as 2.5% on Thursday following the announcement.

Tesla was gaining ground Thursday, its shares up as much as 2.5%, after naming Elon Musk's replacement as board chair.

The electric-car maker has chosen Robyn Denholm, the CFO at the Australian telecom operator Telstra, as its new board chair. Tesla is still searching for two independent directors, according to a company representative. That must be done by December 28 as part of Tesla's settlement with the Securities and Exchange Commission.

"Robyn has extensive experience in both the tech and auto industries, and she has made significant contributions as a Tesla Board member over the past four years in helping us become a profitable company," Musk said.

"I look forward to working even more closely with Robyn as we continue accelerating the advent of sustainable energy."